WIMBLEDON, England — When Cori Gauff, 15, became the youngest qualifier in Wimbledon’s history, the latest superlative in a budding career already full of them, she had a wish.

She said she “would love to share the court with Serena or Venus,” both of whom reached Grand Slam finals as 17-year-olds.

On Monday, in her first appearance in the main draw of a Grand Slam tournament, she will get that wish. Gauff, the youngest player in the women’s singles draw, will play the most tantalizing first-round match at Wimbledon against the oldest player in the draw: 39-year-old Venus Williams, who had reached four of her nine Wimbledon finals before Gauff was born.

It is a fitting destination for the journey steered by Cori Gauff’s parents, Corey and Candi Gauff, who often followed the road map drawn by the Williams family’s patriarch, Richard, including a shared training base of Pompey Park in Delray Beach, Fla.

“The Williams family in general made me realize that it was possible,” said Corey Gauff, who remains his daughter’s primary coach. “There wasn’t a lot of color in the sport, and particularly in our country, African-American girls weren’t playing tennis.”

Like the Williams family, the Gauffs sought the assistance of established coaches to further develop Cori’s talents. When she was 10, Gauff traveled to the Mouratoglou Academy in France to try out for its Champ’Seed Foundation, which provides assistance for aspiring players.

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Cori Gauff, center, who is called Coco, with her parents, Corey, left, and Candi, at the Wimbledon practice courts.CreditJane Stockdale for The New York Times

Patrick Mouratoglou, the academy’s founder, has coached Serena Williams since 2012. He was immediately impressed by Gauff’s athleticism and her toughness, including the way she handled intense interviews designed to test the young players’ resolve.

Gauff has continued to handle the heat of the spotlight admirably, Mouratoglou said.

“Consider the pressure that she has to deal with since a few years already,” he added. “Because she’s making history — at her level, it’s not like Serena — but she’s the youngest to do this, to do that, and the expectations are unbelievable. I’ve seen her very tight and very much under pressure on several occasions. She’s always fighting, and she’s still winning.”

Serena Williams, who trains occasionally at the Mouratoglou Academy, said that she saw some of her own family in Cori Gauff and her family.

“I see her out there working, training, her and her dad; it reminds me of the time where I was out there with my dad,” Williams said. “I can’t help but look inside of myself and be proud and be happy for her.”

Many of the expectations on Gauff come in the form of investments from businesses that have wanted to get in on the ground floor of her career. Roger Federer’s agency, Team8, signed her at 13. She has endorsement contracts with New Balance and the pasta manufacturer Barilla.

Worries over how that pressure could affect young girls whose tennis abilities outpaced their maturity led the WTA to institute an age eligibility rule, which limits the number of tournaments teenagers can play. The successes of Gauff, who was the youngest to reach the United States Open girls’ final two years ago at 13, have renewed debates on the restrictions. She will be allowed to compete at only five more WTA tournaments before her 16th birthday next March. Instead she has played largely on the lower I.T.F. tour.

Mouratoglou called the rule “a mistake,” saying it intensifies the stress during the limited number of tournaments and slows development. The rule is often attributed to the high-profile flameout of the 1990s prodigy Jennifer Capriati.

“The learning experience of a match, there’s nothing that can replace that,” Mouratoglou said. “Of course it’s very difficult when you’re not allowed to play as much as you need to, to gain experience. The pressure: You don’t have the right to mess up one match, because you have so few.”

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Gauff played Amanda Anisimova in the girls final at the 2017 U.S. Open.CreditChang W. Lee/The New York Times

Gauff is proving to be a quick study despite limited time on court. She did not play any tournaments between a second-round loss at French Open qualifying in late May and her arrival to Wimbledon, but she showed significant growth within that month.

Gauff, ranked 301st and given a wild card into the Wimbledon qualifying tournament, started by beating the highest-ranked player in the field, No. 94 Aliona Bolsova, who had reached the fourth round of the French Open. In the final round, Gauff dominated the No. 128 Greet Minnen, 6-1, 6-1.

Gauff credited her success in part to the grass-specific drills, which emphasized slices and coming forward, led by the Mouratoglou Academy coach Jean-Christophe Faurel.

“I prefer to bang from the baseline, but I’m happy he made me do all those weird drills,” she said.

Corey Gauff said the biggest improvements he’d seen in his daughter had been in her demeanor.

“I said, ‘You need to get better at your body language, and I think that stroke will give you a lot more than you think,’ ” he said.

Cori Gauff, who is in high school, has had other assessments to complete during the tournament, including a science test she completed at 11 p.m. the night before her win over Minnen.

Candi Gauff, who like her husband was a collegiate athlete, said her “first priority is to make sure that I am the mom and that I’m raising a teenage daughter.” Candi Gauff added that she wanted to ensure her daughter’s well-being as she faces the challenges of stardom and the attention of social media.

“There’s a lot of moods that a teenage female can go through,” Candi Gauff said. “We’re making sure we acknowledge her development, acknowledge her feelings, and make sure that anything that’s awkward that may be going on is communicated.”

In many ways, she comes off as a typical teenager, like with her fandom of the musician Jaden Smith. She also shows a broad curiosity for current events and history, which defies the assumptions about a tunnel-visioned tennis prodigy.

The link on her Instagram, for example, is to a Unicef news release titled “Children killed, injured, detained and abused amid escalating violence and unrest in Sudan.”

She also has shown a passion for African-American history, including a recent Instagram story about the Juneteenth holiday on June 19, which commemorates the emancipation of slaves.

“During Black History Month I was posting one random fact that you don’t learn at school a day,” Gauff said. “Because there’s so many things that I didn’t know if it wasn’t for the internet and social media.”

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Gauff on the practice courts Saturday. Serena Williams says Gauff reminds her of her sister Venus. CreditJane Stockdale for The New York Times

Her father said the power of her voice will grow along with her game.

“I’ve always challenged her, from the beginning of this when we started, telling her that she’ll be able to change the world with her racket,” Corey Gauff said. “So I’m not going to encourage her, when she gets there, to stick her head in the ground and ignore social issues.”

Looking up at the vibrant blue sky after her final qualifying win on Thursday, he said he hoped that his daughter could keep her mind-set bright even as her surroundings grow more daunting.

“Forget this tournament, Wimbledon, or any tournament: Just go for it in life, and be happy in the moment,” he said. “Don’t stress. You’re not perfect — it’s O.K. Strive for perfection, but don’t think that you are perfect.”

Perfection may be unattainable, but Gauff is already on to something very good.

“I’m thankful that my parents never put any limitations on my goals, because sometimes parents can do that,” she said. “My parents always told me to shoot as high as I wanted to.”

A version of this article appears in print on , Section D, Page 4 of the New York edition with the headline: 15-Year-Old Has Followed Example of the Williamses And Now Will Face One. Order Reprints | Today’s Paper | Subscribe